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Conceptual issues in scaling sensor networks

Conceptual issues in scaling sensor networks. Massimo Franceschetti, UC Berkeley. State of the art on scaling:. Cory Sharp & Shawn Schaffert Shankar Sastry group. PEG ~100 sensor nodes, 1 evader, 2 pursuers. design for complexity. Can we dramatically scale this?. Practical problems

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Conceptual issues in scaling sensor networks

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  1. Conceptual issues in scaling sensor networks Massimo Franceschetti, UC Berkeley

  2. State of the art on scaling: Cory Sharp & Shawn Schaffert Shankar Sastry group PEG ~100 sensor nodes, 1 evader, 2 pursuers

  3. design for complexity Can we dramatically scale this? • Practical problems • Conceptual problems

  4. Percolation theory • Random graphs • Distributed computing • Distributed control • Channel physics • Distributed sampling • Network information theory • Network coding Practice Theory • Connectivity • Routing • Storage • Failures • Packet loss • Malicious behavior • Remote operation

  5. Some conceptual issues • LARGE SCALE CONNECTIVITY • ROUTING • CAPACITY • CONTROL

  6. Connection probability Connection probability 1 1 |x| 2r |x| Continuum percolation Single hop model Random connection model

  7. Multi-hop connectivity model There is a phase transition at a critical node density value

  8. How does the critical density change with the shape of the connection function? g2(x) g1(x) 1 1 |x| 2r |x|

  9. General Tendency When the selection mechanism with which nodes are connected to each other is sufficiently “spread out’’, then few links (in the limit one on average) will suffice to obtain global connectivity. Balister, Bollobas, Walters (2003) Franceschetti, Booth, Cook, Bruck, Meester (2003) D. Dubhashi, O. Haggstrom, A. Panconesi (2003) R. Meester, M. Penrose, A. Sarkar (1997) M. Penrose (1993)

  10. General Tendency In contrast, when connections do not spread out, few links are not enough for connectivity. Xue and P. R. Kumar (2003) O. Haggstrom and R. Meester (1996)

  11. Connection probability 1 |x| Spread out connections (1)

  12. Theorem Franceschetti, Booth, Cook, Bruck, Meester (2003) Forall connection functions “it is easier to reach connectivity in this model of unreliable network” “longer links are trading off for the unreliability of the connection”

  13. Connection probability 1 |x| Spread out connections (2)

  14. Two different spreading strategies Mixture of short and long links Links are made all longer

  15. Theorem Balister, Bollobas, Walters (2003) Franceschetti, Booth, Cook, Bruck, Meester (2003) Consider annuli shapes A(r) of inner radius r, unit area, and critical density For all , there exists a finite , such that A(r*)percolates, for all It is possible to decrease the connectivity threshold by taking a sufficiently large shift !

  16. squashing Shifting What have we learned CNL CNL=average number of connections per node needed for connectivity

  17. What about routing? • Navigation in the small world • Need links at ALL scale lengths !

  18. Intuition: scale invariance Z r2 r1 Model of neighbors density:

  19. Intuition: scale invariance Z r2 r1 Model of neighbors density:

  20. Intuition: scale invariance Z r2 r1 Model of neighbors density:

  21. Intuition: scale invariance Z r2 r1 Slow close to destination Slow far from destination

  22. Theorem Franceschetti & Meester (2003) T e d S

  23. Bottom line T e d S Build routing trees that are scale invariant to route with few hops at all distance scales Want to balance the number of short and long links Need to exploit the “hairy edge” (D. Culler)

  24. Summary • Towards a system theory of large scale networks • Conceptual issues at different levels • Design for complexity strategy • Close the gap between theory and practice

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